Continuity mistake: When Riddler and Two Face are stealing diamonds, the Riddler is holding a large diamond. Two Face comes over to him and produces an even bigger one. However, if you look closely at the shots, the diamond the Riddler holds gets smaller in one cut, and Two Face then pulls out the diamond Riddler was just holding...
Revealing mistake: When Two Face and Riddler enter Wayne Manor, and knock Alfred down. Alfred, unconscious, pushes the dinner tray aside, so the thugs can carry him into the closet.
Continuity mistake: At Edward Nygma's party at the Ritz Gotham there is a fountain with a large version of his "box" on top. When Two-Face comes, he shoots the "box" and destroys it. There should be some parts left over but when Batman falls through the ceiling he lands on the fountain and there's no remains of the "box."
Continuity mistake: In the scene at the circus when the ringmaster announces "The Flying Graysons", Robin's mom is standing on his left side. In the very next shot, she is on his right side. Also, when Robin is doing the "Death Drop", his mom is on his left and his brother is on his right side. After he completes the stunt and he swings back up with his dad, his mom and brother have switched places.
Continuity mistake: When Chris O'Donnell does the laundry and is putting wet clothes on the string, he takes a clothing item and wraps it around his right leg then twists water out of it. When he does this his right foot goes in the air a few inches above the ground but in a closeup to his foot and water falling it is his right foot standing when it should be his left.
Continuity mistake: In the scene in which Edward is first testing his "box", watch Ed's left shoulder. He goes to turn off the machine, then says his line "What a rush." The shot cuts to Ed's boss briefly. When the shot cuts back to Ed, his left shoulder strap, which was present in every other shot, is missing. He even reaches to take the strap off as he starts to say "A very surprising side effect." Apparently, he didn't even notice that it had fallen off.
Continuity mistake: When checking a tape that shows the (fake) suicide of Stickley, Bruce is handed the suicide letter, which was folded in three parts. The next shot shows a clean sheet of paper, with no wrinkles or folds.
Other mistake: The shot showing the vault swinging back to his location is the same that the one where the vault is swinging out, but going backwards.
Continuity mistake: When Edward Nygma is in his apartment after killing Stickley, we see him pasting letters for the next riddle involving the match head. However, when Bruce and Chase are in her office looking at the riddle after it was delivered, you can see the letters are in different positions than the earlier shot.
Continuity mistake: Bruce's hair is much flatter and messier in the garage than in the previous scene outside when Dick is leaving, even though the garage scene happens directly after.
Other mistake: When Batman puts the lit torch to the cable and the cable breaks; the vault goes back into exactly the same place where the helicopter lifted it out from; connected via a grapple that Batman put through the wall. Ignoring the logistics of how this would be possible, it tightens the grapple, which surely, with the weight of the vault, would have ripped itself away from the wall.
Continuity mistake: In the fight scene outside the elevator at the beginning of the movie, there are at least two shots where you see Batman's back without his cape in the way. There are no items whatsoever attached to the back of his belt. Subsequently he manages to pull the stun device and the grappling gun with grappling hook from behind his costume. A previous corrector proposed that the devices could not be seen because they are concealed in "pouches" on Batman's belt. Close inspection of the scene shows that there are no pouches of any kind on his back or concealed in his cape.
Revealing mistake: When the Riddler projects the question mark above the bat signal, two beams can be seen producing the image, except they are slowly tracing the perimeter. If these beams are producing the image, it should only be visible where the beams are touching, and not everywhere else. In order to produce an image and not just two points, beams would need to travel extremely fast to trace the perimeter without leaving gaps. (much the same way images in a lasershow are produced).
Continuity mistake: As the giant safe is being pulled out of the building, a large section of the wall above the hole breaks and starts falling outside the building. The shot cuts to outside and the hole is now back to the same size as before and no chunks of wall are falling. There aren't even any cracks where a piece might break off.